Dynamics of anticorrelation effects in Raman scattering by phonons

Abstract

Abstract. Photan-photon and photon-phonon anticorrelation effects in Raman scattering are studied theoretically. The Heisenberg equations of motion describing Raman scattering are solved in the short-time approximation. The laser, Stokes, anti-Stokes and phonon modes are quantised. The joint normally ordered characteristic functions are evaluated for modes exhibiting anticorrelation effects. The problem of existence of a Glauber-Sudarshan quasi-distribution function related to anticorrelation effects is considered. The magnitude of the anticorrelation effects depends on the initial statistical properties of the photon and phonon modes.

Quantum Statistical Properties of Photon and Phonon Fields in Brillouin Scattering with Intense Pumping

“…In the first step a scattering of coherent photons on phonons is realized providing a photon field directly reflecting the statistics of phonons, in the second step this field is correlated with the scattered field in the actual scattering process . It can be shown-[, using the short-time solution [9,21], that the statistics of laser photons directly reflect the statistics of phonons provided that only anti-Stokes spontaneous scattering occurs [22,23] . Such a solution provides the correct photon-phonon anticorrelation <AWL AWv >= -gnt2 la L I I lav 1 2 up to the second order of g A t appropriate to spontaneous Brillouin scattering .…”

“…The present paper is a continuation of the work presented in [5], where a general description of the quantum statistics in Brillouin scattering were proposed based on the coherent-state technique . Recently, similar models for Raman scattering have been discussed in [6][7][8][9][10] . In [6], Peiina described the phonons as an infinite markoffian reservoir system whose variables have been eliminated in the process of calculation .…”

“…In [7], Pei'ina removed the assumption of frequency matching and discussed the existence of the Glauber-Sudarshan diagonal representation of density matrix . In [8,9], the short-time approximation solutions have been obtained .…”

Raman and Brillouin couplers with losses and phase mismatch

“…Strong coherent pumping of the laser mode was assumed. One effective phonon mode was employed in [16] and a full quantum description including laser modes can be found in [17]. Quantum correlations between Stokes and anti-Stokes fields were studied [18,191 and the correlations between the pump and Stokes fields were considered and measured [20].…”

On the Calculation of Generating Functions in Quantum Optics

“…If it is positive, as for instance in the case of propagation of radiation through random media, the uncertainty of the photon statistics is greater than that of the Poisson statistics corresponding to the coherent state [17,18] . If it is negative the anticorrelation (antibunching) of photons may occur as in optical parametric processes [10,11,19] and in Raman and hyper-Raman scattering [20][21][22][23] . Note that, in the latter case, the average over the initial gaussian statistics of the field leads to a deviation of the actual statistics from the shifted gaussian statistics .…”